Abstract:

Traditional signal acquisition techniques sample band-limited analog
signals above the Nyquist rate, which is related to the highest analog
frequency in the signal. Compressed sensing (CS) is based on the
revelation that optimization routines can reconstruct a sparse signal
from a small number of linear projections of the signal. Therefore,
CS-based techniques can acquire and process sparse signals at much
lower rates. CS offers tremendous potential in applications such as
broadband analog-to-digital conversion, where the Nyquist rate exceeds
the state of the art.

Information theory has numerous insights to offer CS; I will describe
several investigations along these lines. First, distributed
compressed sensing (DCS) provides new distributed signal acquisition
algorithms that exploit both intra- and inter-signal correlation
structures in multi-signal ensembles. DCS is immediately applicable in
sensor networks. Next, we leverage the remarkable success of graph
reduction algorithms and LDPC channel codes to design low-complexity
CS reconstruction algorithms.

Linear measurements play a crucial role not only in compressed sensing
but in disciplines such as finance, where numerous noisy measurements
are needed to estimate various statistical characteristics. Indeed,
many areas of science and engineering seek to extract information from
linearly derived measurements in a computationally feasible manner.
Advances toward a unified theory of linear measurement systems will
enable us to effectively process the vast amounts of data being
generated in our dynamic world.